Each of the 4 possible combinations of the two properties is possible.

Since I didn't find any detailed explanation, I was wondering: How exactly are claims inherited? When does a strong claim become weak upon inheritance? Can an inheritable claim become not inheritable upon inheritance? If yes, when exactly does that happen?

Also, what are the ways “new” claims can be created? I know you can create a claim using Chancellor, and I think you also receive a claim on title if you lose that title in war. Are there other options?